Adaptive multi-step Runge–Kutta–Nyström methods for general second-order ordinary differential equations

In this study, a variable step size formulation of multi-step general Runge–Kutta–Nyström (MSGN) methods to directly integrate general second-order initial value problems (IVPs) is considered. This formula is carried out using an embedded explicit pair where: the higher-order formula is an accurate...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2023-03, Vol.421, p.114874, Article 114874
Main Authors: Abdulsalam, Athraa, Senu, Norazak, Majid, Zanariah Abdul, Nik Long, Nik Mohd Asri
Format: Article
Language:English
Subjects:
Embedded pairs
General second-order differential equations
Multi-step Runge–Kutta–Nyström methods
Root-trees
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Summary:In this study, a variable step size formulation of multi-step general Runge–Kutta–Nyström (MSGN) methods to directly integrate general second-order initial value problems (IVPs) is considered. This formula is carried out using an embedded explicit pair where: the higher-order formula is an accurate and the lower-order formula uses to estimate the local error. Numerical results show that the new methods perform much better in terms of functions evaluations, implementation cost and execution time compared to other existing high quality embedded Runge–Kutta (ERK) methods in the literature.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114874